Non-Integer Bases, Iteration of Continuous Real Maps, and an Arithmetic Self-Similar set

We prove that a recent result of Komornik and Loreti on the smallest real number q in (1,2) such that the number 1 admits a unique q-expansion can be deduced from a result of the authors (1983) on kneading sequences occurring when iterating continuous maps of the interval. We also give arithmetic results related to this problem.

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